Here's some of the details of the edit:
-The entire Alfred/MacGregor's subplot has been taken out.
-*Most* of the cheesy lines have been removed, as well as all the cartoony sound effects.
-Stupid visual elements such as the Bat-skates, the Bat-credit card, butt and crotch shots, etc have been removed.
-most of Bane has been removed, or at least reduced to just seeming to be a genetically mutated henchman (unless you watch through the end credits).
-Batman's character and dialogue has been tweaked to make it appear as if (brace yourself now!) he only speaks when speaking is needed, he seems much more intelligent and seems much more in control of the world and people around him.
-the petty bickering between Batman and Robin has been removed and they act as a team.
-Batgirl, regretfully, could not be fully removed due to her appearence in the final battle. But her character has been reduced and made to seem if both Bruce Wayne and Alfred had a hand in planning her creation as Batgirl.
- All the stupid gangs and motorbike racing scenes were eliminated. They were essentially useless to the plot.
-Ivy remains essentially intact, though now her character seem more manipulative of Freeze. Freeze himself actually plays a lot more sinister when his stupid lines are greatly reduced and things like making his henchmen sing are gone.
-the opening credits have been re-arranged to resemble more of a 'James Bond' structure: Bat logo, right into intense action, after opening action scene the main credit roll.
There's more but that's all I can think of right now!